From ff36e398b9819c580408eb9b7cffe79f33b7853f Mon Sep 17 00:00:00 2001
From: jvangael <jurgen.vangael@gmail.com>
Date: Sun, 26 Jul 2009 15:32:02 +0200
Subject: [PATCH] Added the number theory and sorting classes.

---
 .../Managed.UnitTests.csproj                  |   1 +
 src/Managed.UnitTests/SortingTests.cs         | 162 +++++
 src/Managed/Managed.csproj                    |   1 +
 src/Managed/NumberTheory/IntegerTheory.cs     |   4 +-
 src/Managed/Sorting.cs                        | 574 ++++++++++++++++++
 src/Native.UnitTests/Native.UnitTests.csproj  |   3 +
 src/Native/Native.csproj                      |   3 +
 7 files changed, 746 insertions(+), 2 deletions(-)
 create mode 100644 src/Managed.UnitTests/SortingTests.cs
 create mode 100644 src/Managed/Sorting.cs

diff --git a/src/Managed.UnitTests/Managed.UnitTests.csproj b/src/Managed.UnitTests/Managed.UnitTests.csproj
index b82020d4..a1f55975 100644
--- a/src/Managed.UnitTests/Managed.UnitTests.csproj
+++ b/src/Managed.UnitTests/Managed.UnitTests.csproj
@@ -70,6 +70,7 @@
     <Compile Include="NumberTheoryTests\IntegerTheoryTest.cs" />
     <Compile Include="PrecisionTest.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
+    <Compile Include="SortingTests.cs" />
     <Compile Include="SpecialFunctionsTest\ErfTests.cs" />
     <Compile Include="ThreadingTests\ParallelTest.cs" />
   </ItemGroup>
diff --git a/src/Managed.UnitTests/SortingTests.cs b/src/Managed.UnitTests/SortingTests.cs
new file mode 100644
index 00000000..d623e62d
--- /dev/null
+++ b/src/Managed.UnitTests/SortingTests.cs
@@ -0,0 +1,162 @@
+// <copyright file="SortingTests.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://mathnet.opensourcedotnet.info
+//
+// Copyright (c) 2009 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace MathNet.Numerics.UnitTests
+{
+    using System;
+    using System.Collections.Generic;
+    using System.Text;
+
+    using MbUnit.Framework;
+
+    using MathNet.Numerics;
+
+    [TestFixture]
+    public class SortingTests
+    {
+        [Test]
+        public void TestRandomTupleArraySorting()
+        {
+            const int Len = 0x1 << 10;
+            var random = new Random();
+
+            int[] keys = new int[Len];
+            int[] items = new int[Len];
+            int[] keysCopy = new int[Len];
+
+            for(int i = 0; i < keys.Length; i++)
+            {
+                keys[i] = random.Next();
+                keysCopy[i] = keys[i];
+                items[i] = -keys[i];
+            }
+
+            Sorting.Sort(keys, items);
+
+            for(int i = 1; i < keys.Length; i++)
+            {
+                Assert.IsTrue(keys[i] >= keys[i - 1], "Sort Order - " + i.ToString());
+                Assert.AreEqual(items[i], -keys[i], "Items Permutation - " + i.ToString());
+            }
+
+            for(int i = 0; i < keysCopy.Length; i++)
+            {
+                Assert.IsTrue(Array.IndexOf(keys, keysCopy[i]) >= 0, "All keys still there - " + i.ToString());
+            }
+        }
+
+        [Test]
+        public void TestRandomTupleListSorting()
+        {
+            const int Len = 0x1 << 10;
+            var random = new Random();
+
+            List<int> keys = new List<int>(Len);
+            List<int> items = new List<int>(Len);
+            int[] keysCopy = new int[Len];
+
+            for(int i = 0; i < Len; i++)
+            {
+                int value = random.Next();
+                keys.Add(value);
+                keysCopy[i] = value;
+                items.Add(-value);
+            }
+
+            Sorting.Sort(keys, items);
+
+            for(int i = 1; i < Len; i++)
+            {
+                Assert.IsTrue(keys[i] >= keys[i - 1], "Sort Order - " + i.ToString());
+                Assert.AreEqual(items[i], -keys[i], "Items Permutation - " + i.ToString());
+            }
+
+            for(int i = 0; i < keysCopy.Length; i++)
+            {
+                Assert.IsTrue(keys.IndexOf(keysCopy[i]) >= 0, "All keys still there - " + i.ToString());
+            }
+        }
+
+        [Test]
+        public void TestRandomTripleArraySorting()
+        {
+            const int Len = 0x1 << 10;
+            var random = new Random();
+
+            int[] keys = new int[Len];
+            int[] items1 = new int[Len];
+            int[] items2 = new int[Len];
+            int[] keysCopy = new int[Len];
+
+            for(int i = 0; i < keys.Length; i++)
+            {
+                keys[i] = random.Next();
+                keysCopy[i] = keys[i];
+                items1[i] = -keys[i];
+                items2[i] = keys[i] >> 2;
+            }
+
+            Sorting.Sort(keys, items1, items2);
+
+            for(int i = 1; i < keys.Length; i++)
+            {
+                Assert.IsTrue(keys[i] >= keys[i - 1], "Sort Order - " + i.ToString());
+                Assert.AreEqual(items1[i], -keys[i], "Items1 Permutation - " + i.ToString());
+                Assert.AreEqual(items2[i], keys[i] >> 2, "Items2 Permutation - " + i.ToString());
+            }
+
+            for(int i = 0; i < keysCopy.Length; i++)
+            {
+                Assert.IsTrue(Array.IndexOf(keys, keysCopy[i]) >= 0, "All keys still there - " + i.ToString());
+            }
+        }
+
+        [Test]
+        public void TestAppliedListSorting()
+        {
+            const int Len = 0x1 << 10;
+            var random = new Random();
+
+            List<int> list = new List<int>();
+
+            for(int i = 0; i < Len; i++)
+            {
+                list.Add(random.Next());
+            }
+
+            // default sorting (Ascending)
+            list.Sort();
+
+            // just check that the order is as expected, not that the items are correct
+            for(int i = 1; i < list.Count; i++)
+            {
+                Assert.IsTrue(list[i] >= list[i - 1], "Sort Order - " + i.ToString());
+            }
+        }
+    }
+}
diff --git a/src/Managed/Managed.csproj b/src/Managed/Managed.csproj
index afbb4012..cc486c32 100644
--- a/src/Managed/Managed.csproj
+++ b/src/Managed/Managed.csproj
@@ -79,6 +79,7 @@
     </Compile>
     <Compile Include="SiConstants.cs" />
     <Compile Include="SiPrefixes.cs" />
+    <Compile Include="Sorting.cs" />
     <Compile Include="SpecialFunctions.cs" />
     <Compile Include="SpecialFunctions\Erf.cs" />
     <Compile Include="Threading\AggregateException.cs" />
diff --git a/src/Managed/NumberTheory/IntegerTheory.cs b/src/Managed/NumberTheory/IntegerTheory.cs
index f801b5c2..b14a5eed 100644
--- a/src/Managed/NumberTheory/IntegerTheory.cs
+++ b/src/Managed/NumberTheory/IntegerTheory.cs
@@ -1,4 +1,4 @@
-// <copyright file="IntegerTheory.cs" company="Math.NET">
+// <copyright file="IntegerTheory.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://mathnet.opensourcedotnet.info
 //
@@ -31,7 +31,7 @@ namespace MathNet.Numerics.NumberTheory
     using System;
 
     /// <summary>
-    /// Number Theory for Integers
+    /// Number theory utility functions for integers.
     /// </summary>
     public static class IntegerTheory
     {
diff --git a/src/Managed/Sorting.cs b/src/Managed/Sorting.cs
new file mode 100644
index 00000000..65796790
--- /dev/null
+++ b/src/Managed/Sorting.cs
@@ -0,0 +1,574 @@
+// <copyright file="Sorting.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://mathnet.opensourcedotnet.info
+//
+// Copyright (c) 2009 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace MathNet.Numerics
+{
+    using System;
+    using System.Collections.Generic;
+    using System.Text;
+
+    /// <summary>
+    /// Sorting algorithms for single, tuple and triple lists.
+    /// </summary>
+    public static class Sorting
+    {
+        /// <summary>
+        /// Sort a list of keys, inplace using the quick sort algorithm.
+        /// </summary>
+        /// <typeparam name="T">The type of elements stored in the list.</typeparam>
+        /// <param name="keys">List to sort.</param>
+        public static void Sort<T>(IList<T> keys)
+        {
+            Sort(keys, Comparer<T>.Default);
+        }
+
+        /// <summary>
+        /// Sort a list of keys and items with respect to the keys, inplace using the quick sort algorithm.
+        /// </summary>
+        /// <typeparam name="TKey">The type of elements stored in the key list.</typeparam>
+        /// <typeparam name="TItem">The type of elements stored in the item list.</typeparam>
+        /// <param name="keys">List to sort.</param>
+        /// <param name="items">List to permutate the same way as the key list.</param>
+        public static void Sort<TKey, TItem>(IList<TKey> keys, IList<TItem> items)
+        {
+            Sort(keys, items, Comparer<TKey>.Default);
+        }
+
+        /// <summary>
+        /// Sort a list of keys, items1 and items2 with respect to the keys, inplace using the quick sort algorithm.
+        /// </summary>
+        /// <typeparam name="TKey">The type of elements stored in the key list.</typeparam>
+        /// <typeparam name="TItem1">The type of elements stored in the first item list.</typeparam>
+        /// <typeparam name="TItem2">The type of elements stored in the second item list.</typeparam>
+        /// <param name="keys">List to sort.</param>
+        /// <param name="items1">First list to permutate the same way as the key list.</param>
+        /// <param name="items2">Second list to permutate the same way as the key list.</param>
+        public static void Sort<TKey, TItem1, TItem2>(IList<TKey> keys, IList<TItem1> items1, IList<TItem2> items2)
+        {
+            Sort(keys, items1, items2, Comparer<TKey>.Default);
+        }
+
+        /// <summary>
+        /// Sort a range of a list of keys, inplace using the quick sort algorithm.
+        /// </summary>
+        /// <typeparam name="T">The type of elements in the key list.</typeparam>
+        /// <param name="keys">List to sort.</param>
+        /// <param name="index">The zero-based starting index of the range to sort.</param>
+        /// <param name="count">The length of the range to sort.</param>
+        public static void Sort<T>(IList<T> keys, int index, int count)
+        {
+            Sort(keys, index, count, Comparer<T>.Default);
+        }
+
+        /// <summary>
+        /// Sort a list of keys, inplace using the quick sort algorithm using the quick sort algorithm.
+        /// </summary>
+        /// <typeparam name="T">The type of elements in the key list.</typeparam>
+        /// <param name="keys">List to sort.</param>
+        /// <param name="comparer">Comparison, defining the sort order.</param>
+        public static void Sort<T>(IList<T> keys, IComparer<T> comparer)
+        {
+            if(null == keys)
+            {
+                throw new ArgumentNullException("keys");
+            }
+
+            if(null == comparer)
+            {
+                throw new ArgumentNullException("comparer");
+            }
+
+            // basic cases
+            if(keys.Count <= 1)
+            {
+                return;
+            }
+
+            if(keys.Count == 2)
+            {
+                if(comparer.Compare(keys[0], keys[1]) > 0)
+                {
+                    Swap(keys, 0, 1);
+                }
+
+                return;
+            }
+
+            // generic list case
+            List<T> list = keys as List<T>;
+            if(null != list)
+            {
+                list.Sort(comparer);
+                return;
+            }
+
+            // array case
+            T[] array = keys as T[];
+            if(null != array)
+            {
+                Array.Sort(array, comparer);
+                return;
+            }
+
+            // local sort implementation
+            QuickSort(keys, comparer, 0, keys.Count - 1);
+        }
+
+        /// <summary>
+        /// Sort a list of keys and items with respect to the keys, inplace using the quick sort algorithm.
+        /// </summary>
+        /// <typeparam name="TKey">The type of elements in the key list.</typeparam>
+        /// <typeparam name="TItem">The type of elements in the item list.</typeparam>
+        /// <param name="keys">List to sort.</param>
+        /// <param name="items">List to permutate the same way as the key list.</param>
+        /// <param name="comparer">Comparison, defining the sort order.</param>
+        public static void Sort<TKey, TItem>(IList<TKey> keys, IList<TItem> items, IComparer<TKey> comparer)
+        {
+            if(null == keys)
+            {
+                throw new ArgumentNullException("keys");
+            }
+
+            if(null == items)
+            {
+                throw new ArgumentNullException("items");
+            }
+
+            if(null == comparer)
+            {
+                throw new ArgumentNullException("comparer");
+            }
+
+            // array case
+            TKey[] keysArray = keys as TKey[];
+            TItem[] itemsArray = items as TItem[];
+            if((null != keysArray) && (null != itemsArray))
+            {
+                Array.Sort(keysArray, itemsArray, comparer);
+                return;
+            }
+
+            // local sort implementation
+            QuickSort(keys, items, comparer, 0, keys.Count - 1);
+        }
+
+        /// <summary>
+        /// Sort a list of keys, items1 and items2 with respect to the keys, inplace using the quick sort algorithm.
+        /// </summary>
+        /// <typeparam name="TKey">The type of elements in the key list.</typeparam>
+        /// <typeparam name="TItem1">The type of elements in the first item list.</typeparam>
+        /// <typeparam name="TItem2">The type of elements in the second item list.</typeparam>
+        /// <param name="keys">List to sort.</param>
+        /// <param name="items1">First list to permutate the same way as the key list.</param>
+        /// <param name="items2">Second list to permutate the same way as the key list.</param>
+        /// <param name="comparer">Comparison, defining the sort order.</param>
+        public static void Sort<TKey, TItem1, TItem2>(
+            IList<TKey> keys, IList<TItem1> items1, IList<TItem2> items2, IComparer<TKey> comparer)
+        {
+            if(null == keys)
+            {
+                throw new ArgumentNullException("keys");
+            }
+
+            if(null == items1)
+            {
+                throw new ArgumentNullException("items1");
+            }
+
+            if(null == items2)
+            {
+                throw new ArgumentNullException("items2");
+            }
+
+            if(null == comparer)
+            {
+                throw new ArgumentNullException("comparer");
+            }
+
+            // local sort implementation
+            QuickSort(keys, items1, items2, comparer, 0, keys.Count - 1);
+        }
+
+        /// <summary>
+        /// Sort a range of a list of keys, inplace using the quick sort algorithm.
+        /// </summary>
+        /// <typeparam name="T">The type of element in the list.</typeparam>
+        /// <param name="keys">List to sort.</param>
+        /// <param name="index">The zero-based starting index of the range to sort.</param>
+        /// <param name="count">The length of the range to sort.</param>
+        /// <param name="comparer">Comparison, defining the sort order.</param>
+        public static void Sort<T>(IList<T> keys, int index, int count, IComparer<T> comparer)
+        {
+            if(null == keys)
+            {
+                throw new ArgumentNullException("keys");
+            }
+
+            if(null == comparer)
+            {
+                throw new ArgumentNullException("comparer");
+            }
+
+            if(index < 0 || index >= keys.Count)
+            {
+                throw new ArgumentOutOfRangeException("index");
+            }
+
+            if(count < 0 || index + count > keys.Count)
+            {
+                throw new ArgumentOutOfRangeException("count");
+            }
+
+            // basic cases
+            if(count <= 1)
+            {
+                return;
+            }
+
+            if(count == 2)
+            {
+                if(comparer.Compare(keys[index], keys[index + 1]) > 0)
+                {
+                    Swap(keys, index, index + 1);
+                }
+
+                return;
+            }
+
+            // generic list case
+            List<T> list = keys as List<T>;
+            if(null != list)
+            {
+                list.Sort(index, count, comparer);
+                return;
+            }
+
+            // array case
+            T[] array = keys as T[];
+            if(null != array)
+            {
+                Array.Sort(array, index, count, comparer);
+                return;
+            }
+
+            // local sort implementation
+            QuickSort(keys, comparer, index, count - 1);
+        }
+
+        /// <summary>
+        /// Recursive implementation for an inplace quick sort on a list.
+        /// </summary>
+        /// <typeparam name="T">The type of the list on which the quick sort is performed.</typeparam>
+        /// <param name="keys">The list which is sorted using quick sort.</param>
+        /// <param name="comparer">The method with which to compare two elements of the quick sort.</param>
+        /// <param name="left">The left boundary of the quick sort.</param>
+        /// <param name="right">The right boundary of the quick sort.</param>
+        private static void QuickSort<T>(IList<T> keys, IComparer<T> comparer, int left, int right)
+        {
+            do
+            {
+                // Pivoting
+                int a = left;
+                int b = right;
+                int p = a + ((b - a) >> 1); // midpoint
+
+                if(comparer.Compare(keys[a], keys[p]) > 0)
+                {
+                    Swap(keys, a, p);
+                }
+
+                if(comparer.Compare(keys[a], keys[b]) > 0)
+                {
+                    Swap(keys, a, b);
+                }
+
+                if(comparer.Compare(keys[p], keys[b]) > 0)
+                {
+                    Swap(keys, p, b);
+                }
+
+                T pivot = keys[p];
+
+                // Hoare Partitioning
+                do
+                {
+                    while(comparer.Compare(keys[a], pivot) < 0)
+                    {
+                        a++;
+                    }
+
+                    while(comparer.Compare(pivot, keys[b]) < 0)
+                    {
+                        b--;
+                    }
+
+                    if(a > b)
+                    {
+                        break;
+                    }
+
+                    if(a < b)
+                    {
+                        Swap(keys, a, b);
+                    }
+
+                    a++;
+                    b--;
+                }
+                while(a <= b);
+
+                // In order to limit the recusion depth to log(n), we sort the 
+                // shorter partition recusively and the longer partition iteratively.
+                if((b - left) <= (right - a))
+                {
+                    if(left < b)
+                    {
+                        QuickSort(keys, comparer, left, b);
+                    }
+
+                    left = a;
+                }
+                else
+                {
+                    if(a < right)
+                    {
+                        QuickSort(keys, comparer, a, right);
+                    }
+
+                    right = b;
+                }
+            }
+            while(left < right);
+        }
+
+        /// <summary>
+        /// Recursive implementation for an inplace quick sort on a list while reordering one other list accordingly.
+        /// </summary>
+        /// <typeparam name="T">The type of the list on which the quick sort is performed.</typeparam>
+        /// <typeparam name="TItems">The type of the list which is automatically reordered accordingly.</typeparam>
+        /// <param name="keys">The list which is sorted using quick sort.</param>
+        /// <param name="items">The list which is automatically reordered accordingly.</param>
+        /// <param name="comparer">The method with which to compare two elements of the quick sort.</param>
+        /// <param name="left">The left boundary of the quick sort.</param>
+        /// <param name="right">The right boundary of the quick sort.</param>
+        private static void QuickSort<T, TItems>(IList<T> keys, IList<TItems> items, IComparer<T> comparer, int left, int right)
+        {
+            do
+            {
+                // Pivoting
+                int a = left;
+                int b = right;
+                int p = a + ((b - a) >> 1); // midpoint
+
+                if(comparer.Compare(keys[a], keys[p]) > 0)
+                {
+                    Swap(keys, a, p);
+                    Swap(items, a, p);
+                }
+
+                if(comparer.Compare(keys[a], keys[b]) > 0)
+                {
+                    Swap(keys, a, b);
+                    Swap(items, a, b);
+                }
+
+                if(comparer.Compare(keys[p], keys[b]) > 0)
+                {
+                    Swap(keys, p, b);
+                    Swap(items, p, b);
+                }
+
+                T pivot = keys[p];
+
+                // Hoare Partitioning
+                do
+                {
+                    while(comparer.Compare(keys[a], pivot) < 0)
+                    {
+                        a++;
+                    }
+
+                    while(comparer.Compare(pivot, keys[b]) < 0)
+                    {
+                        b--;
+                    }
+
+                    if(a > b)
+                    {
+                        break;
+                    }
+
+                    if(a < b)
+                    {
+                        Swap(keys, a, b);
+                        Swap(items, a, b);
+                    }
+
+                    a++;
+                    b--;
+                }
+                while(a <= b);
+
+                // In order to limit the recusion depth to log(n), we sort the 
+                // shorter partition recusively and the longer partition iteratively.
+                if((b - left) <= (right - a))
+                {
+                    if(left < b)
+                    {
+                        QuickSort(keys, items, comparer, left, b);
+                    }
+
+                    left = a;
+                }
+                else
+                {
+                    if(a < right)
+                    {
+                        QuickSort(keys, items, comparer, a, right);
+                    }
+
+                    right = b;
+                }
+            }
+            while(left < right);
+        }
+
+        /// <summary>
+        /// Recursive implementation for an inplace quick sort on one list while reordering two other lists accordingly.
+        /// </summary>
+        /// <typeparam name="T">The type of the list on which the quick sort is performed.</typeparam>
+        /// <typeparam name="TItems1">The type of the first list which is automatically reordered accordingly.</typeparam>
+        /// <typeparam name="TItems2">The type of the second list which is automatically reordered accordingly.</typeparam>
+        /// <param name="keys">The list which is sorted using quick sort.</param>
+        /// <param name="items1">The first list which is automatically reordered accordingly.</param>
+        /// <param name="items2">The second list which is automatically reordered accordingly.</param>
+        /// <param name="comparer">The method with which to compare two elements of the quick sort.</param>
+        /// <param name="left">The left boundary of the quick sort.</param>
+        /// <param name="right">The right boundary of the quick sort.</param>
+        private static void QuickSort<T, TItems1, TItems2>(
+            IList<T> keys, IList<TItems1> items1, IList<TItems2> items2, IComparer<T> comparer, int left, int right)
+        {
+            do
+            {
+                // Pivoting
+                int a = left;
+                int b = right;
+                int p = a + ((b - a) >> 1); // midpoint
+
+                if(comparer.Compare(keys[a], keys[p]) > 0)
+                {
+                    Swap(keys, a, p);
+                    Swap(items1, a, p);
+                    Swap(items2, a, p);
+                }
+
+                if(comparer.Compare(keys[a], keys[b]) > 0)
+                {
+                    Swap(keys, a, b);
+                    Swap(items1, a, b);
+                    Swap(items2, a, b);
+                }
+
+                if(comparer.Compare(keys[p], keys[b]) > 0)
+                {
+                    Swap(keys, p, b);
+                    Swap(items1, p, b);
+                    Swap(items2, p, b);
+                }
+
+                T pivot = keys[p];
+
+                // Hoare Partitioning
+                do
+                {
+                    while(comparer.Compare(keys[a], pivot) < 0)
+                    {
+                        a++;
+                    }
+
+                    while(comparer.Compare(pivot, keys[b]) < 0)
+                    {
+                        b--;
+                    }
+
+                    if(a > b)
+                    {
+                        break;
+                    }
+
+                    if(a < b)
+                    {
+                        Swap(keys, a, b);
+                        Swap(items1, a, b);
+                        Swap(items2, a, b);
+                    }
+
+                    a++;
+                    b--;
+                }
+                while(a <= b);
+
+                // In order to limit the recusion depth to log(n), we sort the 
+                // shorter partition recusively and the longer partition iteratively.
+                if((b - left) <= (right - a))
+                {
+                    if(left < b)
+                    {
+                        QuickSort(keys, items1, items2, comparer, left, b);
+                    }
+
+                    left = a;
+                }
+                else
+                {
+                    if(a < right)
+                    {
+                        QuickSort(keys, items1, items2, comparer, a, right);
+                    }
+
+                    right = b;
+                }
+            }
+            while(left < right);
+        }
+
+        /// <summary>
+        /// Performs an in place swap of two elements in a list.
+        /// </summary>
+        /// <typeparam name="T">The type of elements stored in the list.</typeparam>
+        /// <param name="keys">The list in which the elements are stored.</param>
+        /// <param name="a">The index of the first element of the swap.</param>
+        /// <param name="b">The index of the second element of the swap.</param>
+        internal static void Swap<T>(IList<T> keys, int a, int b)
+        {
+            T local = keys[a];
+            keys[a] = keys[b];
+            keys[b] = local;
+        }
+    }
+}
diff --git a/src/Native.UnitTests/Native.UnitTests.csproj b/src/Native.UnitTests/Native.UnitTests.csproj
index 38c98b47..8422f4e0 100644
--- a/src/Native.UnitTests/Native.UnitTests.csproj
+++ b/src/Native.UnitTests/Native.UnitTests.csproj
@@ -89,6 +89,9 @@
     <Compile Include="..\Managed.UnitTests\PrecisionTest.cs">
       <Link>PrecisionTest.cs</Link>
     </Compile>
+    <Compile Include="..\Managed.UnitTests\SortingTests.cs">
+      <Link>SortingTests.cs</Link>
+    </Compile>
     <Compile Include="..\Managed.UnitTests\SpecialFunctionsTest\ErfTests.cs">
       <Link>SpecialFunctionsTest\ErfTests.cs</Link>
     </Compile>
diff --git a/src/Native/Native.csproj b/src/Native/Native.csproj
index 63fca844..889aa344 100644
--- a/src/Native/Native.csproj
+++ b/src/Native/Native.csproj
@@ -131,6 +131,9 @@
     <Compile Include="..\Managed\SiPrefixes.cs">
       <Link>SiPrefixes.cs</Link>
     </Compile>
+    <Compile Include="..\Managed\Sorting.cs">
+      <Link>Sorting.cs</Link>
+    </Compile>
     <Compile Include="..\Managed\SpecialFunctions.cs">
       <Link>SpecialFunctions.cs</Link>
     </Compile>